1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tigry1 [53]
3 years ago
15

verify that the fucntion satisfies the three hypotheses of rolles theorem on the given interval . then find all numbers c that s

atisfy the conclusion . f(x)= x^3-2x^2-4x+2 . [ -2,2]
Mathematics
1 answer:
Ghella [55]3 years ago
4 0

The roots of the polynomial <span><span>x^3 </span>− 2<span>x^2 </span>− 4x + 2</span> are:

<span><span>x1 </span>= 0.42801</span>

<span><span>x2 </span>= −1.51414</span>

<span><span>x3 </span>= 3.08613</span>


x1 and x2 are in the desired interval [-2, 2]

f'(x) = 3x^2 - 4x - 4

so we have:

3x^2 - 4x - 4 = 0

<span>x = ( 4 +- </span><span>√(16 + 48) </span>)/6

x_1 = -4/6 = -0.66

x_ 2 = 2

According to Rolle's theorem, we have one point in between:

x1 = 0.42801 and x2 = −1.51414

where f'(x) = 0, and that is <span>x_1 = -0.66</span>

so we see that Rolle's theorem holds in our function.

You might be interested in
50 POINTS
mamaluj [8]

Answer:

The answer is below

Step-by-step explanation:

The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds: A linear model with ordered pairs at 0, 60 and 2, 75 and 4, 75 and 6, 40 and 8, 20 and 10, 0 and 12, 0 and 14, 0. The x axis is labeled Time in seconds, and the y axis is labeled Height in feet. Part A: During what interval(s) of the domain is the water balloon's height increasing? (2 points) Part B: During what interval(s) of the domain is the water balloon's height staying the same? (2 points) Part C: During what interval(s) of the domain is the water balloon's height decreasing the fastest? Use complete sentences to support your answer. (3 points) Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 16 seconds.

Answer:

Part A:

Between 0 and 2 seconds, the height of the balloon increases from 60 feet to 75 feet  at a rate of 7.5 ft/s

Part B:

Between 2 and 4 seconds, the height stays constant at 75 feet.

Part C:

Between 4 and 6 seconds, the height of the balloon decreases from 75 feet to 40 feet at a rate of -17.5 ft/s

Between 6 and 8 seconds, the height of the balloon decreases from 40 feet to 20 feet at a rate of -10 ft/s

Between 8 and 10 seconds, the height of the balloon decreases from 20 feet to 0 feet at a rate of -10 ft/s

Hence it fastest decreasing rate is -17.5 ft/s which is between 4 to 6 seconds.

Part D:

From 10 seconds, the balloon is at the ground (0 feet), it continues to remain at 0 feet even at 16 seconds.

3 0
3 years ago
A page was missing from a 72 - page book. When Josh added up the remaining page numbers, the sum was 2521. Which page was missin
morpeh [17]
The numbers 1 to 72 add up to (1+72) x 72/2 = 73 x 36 = 2628
If we take away what Josh got we have 2628 - 2521 = 107
Pages in a book are odd on the first side and even on the second, so pages 11 and 12 are on the same sheet.
107 / 2 = 53.5 so the missing page had 53 on one side and 54 on the other side.
The remaining pages would have been numbered 1, 2, 3, ..., 51, 52, 55, 56, ... 71, 72
8 0
3 years ago
the average rainfall in Clearview is 38 inches . this year 29.777 inches fell . How much less rain fell this year than falls in
dexar [7]
38 (average) - 29.777 (this year) = 8.223 inches less this year than the average year.
6 0
3 years ago
How many times can 475 go into 1,662?
Solnce55 [7]
3.498947368421053 <- Exactly...

Evenly: Three times. It comes out to be 1425 with 237 left...

I hope this answers your question... Let me know if I didn't! <3 


7 0
3 years ago
Read 2 more answers
Solve: -19 = X - 19 halppppp
Juliette [100K]

Answer:

x = 0

Step-by-step explanation:

Step 1: Write equation

-19 = x - 19

Step 2: Solve for <em>x</em>

  1. Add 19 to both sides: 0 = x
  2. Rewrite: x = 0

Step 3: Check

<em>Plug in x to verify it's a solution.</em>

-19 = 0 - 19

-19 = -19

3 0
3 years ago
Read 2 more answers
Other questions:
  • Determine whether the following sequence is geometric. If​ so, find the common ratio.
    7·1 answer
  • Determine the image of the point (1, 5) under a rotation of 180° about the origin
    14·1 answer
  • What multiplication expression can you use to solve 627÷11?
    14·2 answers
  • Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary.
    9·1 answer
  • Anthony buys 4 pairs of shoes how many individual shoes did he buy
    11·2 answers
  • The sides of a triangle measures 6 inches, 8inches, and 10inches. The triangle has one 90 degree angle. What type of triangle is
    11·1 answer
  • the vertex of this parabola is at (2,-1). when the y-value is 0, the x-value is 5. what is the coefficient of the squared term i
    14·1 answer
  • Determine the length of the segment with endpoints C(1, 4) and D(11, 28).
    12·1 answer
  • Another customer calls you wanting to know how much fence they should install around the circumference of their circular garden
    15·1 answer
  • Which expressions are equivalent to 2 ln a 2 ln b - ln a? Check all that apply. Ln ab2 - ln a ln a 2 ln b ln a2 ln b2 - ln a 2 l
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!